code: def _dot_convolve(a1, a2, mode):
      offset = 0
      if a1.size < a2.size:
          a1, a2 = a2, a1
          offset = 1 - a2.size % 2
  
      dtype = cupy.result_type(a1, a2)
      n1, n2 = a1.size, a2.size
      a1 = a1.astype(dtype, copy=False)
      a2 = a2.astype(dtype, copy=False)
  
      if mode == "full":
          out_size = n1 + n2 - 1
          a1 = cupy.pad(a1, n2 - 1)
      elif mode == "same":
          out_size = n1
          pad_size = (n2 - 1) // 2 + offset
          a1 = cupy.pad(a1, (n2 - 1 - pad_size, pad_size))
      elif mode == "valid":
          out_size = n1 - n2 + 1
  
      stride = a1.strides[0]
      a1 = stride_tricks.as_strided(
          a1, (out_size, n2), (stride, stride)
      )
      output = _dot_kernel(a1, a2[::-1], axis=1)
      return output
  
file_path: cupy/cupy/_math/misc.py
imports: import cupy
  import cupyx.scipy.fft
  from cupy import _core
  from cupy._core import _routines_math
  from cupy._core import fusion
  from cupy.lib import stride_tricks
  import numpy
label_desc: Use image node_id 5 for calling a global function with example usage: _dot_convolve(a1, a2, mode) and returns: output